If \(q\ge 1\)  and \(v_1=v_{q+1}\) , then this path is called a cycle of length \(q\) . A hypergraph \(H\)  is connected if there exists a path starting at \(v\)  and terminating at \(u\)  for all \(v,u\in V\) , and is called acyclic if it contains no cycle. The other undefined definitions here can refer to [1]} and [2]}.
